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Work Rate Questions - I collected from GMAT Club [#permalink]

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29 Nov 2008, 09:37

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Hello GMAT Club'rs

I collected some questions in the Work Rate area from the GMAT Club posts. Thought I would put it all together for someone who needs a little more practise in this area. You can search for all these questions in the Forum.

Happy Solving... LS

1.Working, independently X takes 12 hours to finish a certain work. he finishes 2/3 of the work . The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finsh his work?

2.Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A. 4 B. 6 C. 8 D. 10 E. 12

3.Working together, printer A and printer B would finish the task in 24 minutes. Printer A alone would finish the task in 60 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ? 1:600 2:800 3:1000 4:1200 5:1500

4.25 men reap a field in 20 days . when should 15 men leave the work.if the whole field is to be reaped in 37-1/2 days after they leave the work?

A 5 days B 10 days

5.Read the question from the diagram above and C 7 days D 7-1/2 days

6.when a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? 3/10 2/5 1/2 2/3 6/5

7.If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost? (1) Tom makes 20% less per hour than Jim does. (2) x + y = $43.75

8.A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened? * at 2:00 pm * at 2:30 pm * at 3:00 pm * at 3:30 pm * at 4:00 pm

9.With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first? * 9000 cubic meters * 10500 cubic meters * 11750 cubic meters * 12000 cubic meters * 12500 cubic meters

10.It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages? * 12 * 18 * 20 * 24 * 30

11.6 machines each working at the same constant rate together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

12.At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? A. 2/3 B. 1 C. 3/4 D. 3/2 E. 2

13.Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours. How many hours will it take A to finish the work independently? (1) Working together, A and B can finish the work in 4 hours. (2) Working together, B and C can finish the work in 48/7 hours.

14.John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?

15.working together at their constant rates , A and B can fill an empty tank to capacity in1/2 hr.what is the constant rate of pump B? 1) A's constant rate is 25LTS / min 2) the tanks capacity is 1200 lts.

16.Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

1/3x 3x/x-3 x-3/3x x/x-3 x-3/x

17.Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job? 18 13+1/2 7+1/5 4+1/2 3+2/3

18.Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A) 2 B) 3 C) 4 D) 6 E) 8

19.Machince A and B are each used to manufacture 660 sprockets. It takes A 10 hours longer to produce 660 sprockets than machine B. B produces 10 percent more sprockets per hour than A. How many sprockets per hours does machine A produce? A. 6 B. 6.6 C. 60 D. 100 E 110

20.A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

a) 3

b) 4

c) 6

d) 9

e) 12

21.One hour after Yolanda started walking from X to Y, a distance of 45 miiles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles /hour and Bob's was 4 miles / hour, how many miles had Bab walked when they met?

24 23 22 21 19.5

22.Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

25% 33 1/3% 50% 66 2/3% 75%

23.Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 12 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.

80 days 100 days 120 days 110 days 90 days

24.Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately. 26days 27days 23days 25days 24 days

25.A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?

28 30 33 36 38

26.Working together, John and Jack can type 20 pages in one hour. They will be able to type 22 pages in one hour if Jack increases his typing speed by 25%. What is the ratio of Jack's normal typing speed to that of John? 1/3 2/5 1/2 2/3 3/5

27.Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?

28.Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

29.One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?

(A) 5/7 (B) 1 (C) 10/7 (D) 12/7 (E) 22/7

30.Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? A.7/17 B.14/31 C. 7/15 D.17/35 E.1/2

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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My solutions, hopefully I've saved you some time instead of searching for every answer (they should all be correct since I've verified them). Thanks for the questions, I've learned some new tricks

Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?

Lindsay paint 1/x in 20 min so 3/x in 60 min

Together they paint 3/x + j = 1 in 60 min

J = 1 - 3/x J = x/x - 3/x J = x-3/x in 60 min so in 20 min he will only paint a third (20/60 = 1/3) 1/3 * (x-3)/x answer: (x-3)/3x

Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

X work rate 1/9

X worked for 3 hours + x+y worked for 4 hours and completed 1 work 3*(1/9) + 4(1/9 + 1/y) = 1 (1/3)*(1/4)+ (1/9 + 1/y) = 1/4 1/9 + 1/y = 3/12 - 1/12 => 1/9 + 1/y = 1/6 1/y = 1/18

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

Rate for six machines 1/12 (they do 1/12 of the work in 1 day or 1 work in 12 days) Rate for one machine 1/12 * 6 = 1/72 (so 6 machines working 1/72 is 6*1/72 or 1/12 which is correct)

To complete the work in 8 days we need a rate of 1/8, so how many machines do we need to get a rate of 1/8 ? (1/72)*x = 1/8 x = 72/8 x = 9

If 6 can complete the work in 12 days 9 can complete it in 8 days, so three more.

Machince A and B are each used to manufacture 660 sprockets. It takes A 10 hours longer to produce 660 sprockets than machine B. B produces 10 percent more sprockets per hour than A. How many sprockets per hours does machine A produce?

A produces x sprockets per hour B produces x * 1,1 (11/10) sprockets per hour

Let y denote hour B produces rate * time = work => 1,1x sprockets * y yours = 660 sprockets It takes A hours more to produces the same amount so x * (y+10) = 660

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

Rate R 1/36 Rate S 1/18

x = number of machines

So how many machines do we need to complete the work in 2 hours or equivalent, have a rate of 1/2?

One hour after Yolanda started walking from X to Y, a distance of 45 miiles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles /hour and Bob's was 4 miles / hour, how many miles had Bab walked when they met?

Yolanda = 3mph Bob = 4 mph

Yolanda started one hour before Bob, so you could say that they started at the same time with only 42 miles left

When they meet the will have walked for the same hours x but the distance will differ so

Yolanda will walk (rate * time = distance) 3 mph * x hours = y miles

Bob 4 mph * x hours = (42 - y miles) since he is walking in the opposite direction

1) 3x = y 2) 4x = (42-y)

1) x = y/3 using that in 2)

2) 4y/3 = 42 - y 7y/3 = 42 y = 18 (which is the distance Yolanda have walked so for Bob it is 42-18 which is 24)

Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

Kartons per hour would be the measurement Lets denote the machines A and B (the faster one)

A produce at a rate of k/8 = A B produce at a rate of k/4 = B

Rearranging: 8A = k 4B = k

8A = 4B 2A = B Ratio B/A = 2/1 so together they produce (2+1=3) and B solely produces 2/3 of the boxes

This problem could be solved without any calculations at all. If I work twice as fast as someone else and together we produce 1 or 100, the equation will always look like x + 2x = 1 which is 33.33... + 66.66... = 1

Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 12 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.

Together they compete the work in 20 days (so 1 work in 20 days or work at a rate of 1/20 together)

1) (1/A + 1/M) = 1/20

The second equation: Working together for 12 days and then Adam works single for 10 days to complete the work so

2) 12(1/A + 1/M) + 10(1/A) = 1

Substituting the the left side in 1) into 2)

12(1/20) + 10/a = 1 12/20 +10/a = 20/20 10/a = 8/20 200 = 8a a = 25 which is Adams rate when working alone, put into 1)

1/25 + 1/m = 1/20 4/100 + 1/m = 5/100 1/m = 1/100

So Michaels rate is 1/100 or equivalent, it takes him 100 days to complete the work alone

A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?

To calculate average miles per gallon we need total miles and total gallons

City 25 mpg or 1/25 gallon per mile Highway 50 mpg or 1/40 gallon per mile

10 miles in city * 1/25 miles per gallon = 10/25 gallons = 2/5 = 8/20 50 miles on highway * 1/40 miles per gallon = 50/40 gallons = 5/4 = 25/20

Total no of miles 10+50 = 60 Total gallons = 33/20

(60/1)/(33/20) = 60*20/33 = 20*3*20/3*11 = 400/11 which is approximately 36 miles per gallon

Working together, John and Jack can type 20 pages in one hour. They will be able to type 22 pages in one hour if Jack increases his typing speed by 25%. What is the ratio of Jack's normal typing speed to that of John?

Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?

Rates: Tom = 1/6 Peter = 1/3 = 2/6 John = 1/2 = 3/6

1 hours Tom + 1 hour (Tom+Peter) + x hours (Tom+Peter+John) = 1

First we need to solve for X

1 hours (1/6) + 1 hour * (3/6) + x(6/6) = 1 (they will work for <1 hour all three of them)

4/6 + x = 1 x = 2/6

So they will work for 1/3 of an hour or 20 minutes all three of them

Peter will work for 1 hour (with Tom) and 1/3 of an hour with the rest of the guys

In one hour he'll produce 1/3 and in 1/3 of an hour (1/3 * 1/3) = 1/9 of the work

So in total Peter will produce 4/9 of the total work.

Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4hours as machine Y produced in 3 hours.

B is sufficient here

rate * time = number of bottles x working for 4 hours produces z bottles and y working for 3 hours produces only half of that

y * 3 = z bottles x * 4 = 2z bottles (twice the amount)

3y = 4x/2 6y = 4x x/y = 6/4 = 3/2

So when X produce 3 Y produce only 2 and together 5, we can calculate the rest if we want to.

One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?

Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?

Basic: 2/3 of the total Deluxe 1/3 of the total

Basic 5/5 hours to produce Deluxe 7/5 hours to produce

We only produce basic + deluxe so that is the total and we need deluxe/total to find the fraction

Hours spent on deluxe = 7/5 * 1/3 = 7/15 Hours spent on basic = 5/5 * 2/3 = 2/3 = 10/15 Total = 17/15

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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06 Feb 2011, 08:41

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theptrk: Regarding 8) I think this approach is doable in 30s-1min

Fill rate 1/4 and drain rate 1/5, we know that the fill process will be going on for 10 hours, but we don't know how long the draining process will go on. We can see it as two pumps A and B, whereas A pump in and B out

Pump A * 10 hours - Pump B out * x hours = 1 (results in 1 work, or pool filled)

(1/4) * 10 - (1/5) * x = 1 => 50 -4x = 20 => 30 = 4x => x = 7,5 so Pump B will work for 7,5 hours. So if the work was complete at 11 pm B started (11-7,5) 3:30 PM
_________________

Here’s how to solve OG Data Sufficiency #112, Rate Problem in < 1 minute

Quote:

112. Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot? (1) Machine X produced 30 bottles per minute. (2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

Think of this as D=RT

Only, here we have distance = the entire production R is split into the rate for X, and the rate for Y. T is split into 4 hours for X, and 3 hours for Y.

So the entire production = 4 hours @ rate X + 3 hours @ rate Y = 4X + 3Y

The question asks us how many hours of X is required for the entire production?

Well, we already know the entire production is 4X + 3Y, so we set that = (? hours) @ rate X

4X + 3Y = (?) X

So we have 3 pieces: 2 variables (X, Y) and 1 missing number (?)

(1) tells us what X is. Do you really think you can solve 1 equation with 2 variables? NO!! You need more information.

So (1) is no good. Don’t even need to think of anything else.

Let’s look at (2): X produces twice as many bottles in 4 hours as Y in 3 hours. Oh, so they’re telling you what X is in relation to Y.

Well, that would help you rewrite the equation: 4X + 3Y = (?)X

in terms of just (X’s and the ?) or (Y’s and the ?)

I don’t know the calculations, but it would like something like:

4X + somethingX = (?) X combine and you get

(somethingX) = (?)X

Oh wait, there’s X on both sides. If you cancel out the X’s, you’ll end up with some number. I don’t know what that number is, but at this point, I can confidently say that (2) gives me enough information.

(2) gave me X in terms of Y and vice versa. From there, I can get rid of one variable, and be left 1 variable. So I have 1 equation and 1 unknown – I just need that missing number (?). We know 1 equation/1 unknown is solvable, and then from there you can get the actual number.

Don’t waste time thinking about what that number is. Just know that you have enough info to solve the problem with (2).

When (1) is no good and (2) is good, then choose (B) as your final answer.

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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19 Nov 2009, 00:03

The foll questions posted by LS do not appear elsewhere.

Does anyone have the AC and knows the correct answer?

Thanks

1.Working, independently X takes 12 hours to finish a certain work. he finishes 2/3 of the work . The rest of the work is finished by Y whose rate is 1/10 th of X. In how much time does Y finsh his work?

Working together at their respective rates, machine A, B, and C can finish a certain work in 8/3 hours. How many hours will it take A to finish the work independently? (1) Working together, A and B can finish the work in 4 hours. (2) Working together, B and C can finish the work in 48/7 hours.

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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19 Aug 2010, 16:27

Hello,

Could someone please tell me the level of difficulty for the problems above? I have been working problems from various sources (MGMAT, GMAC and an Algebra book) and had trouble with these. FYI, this is overall driving me crazy. There seems to be a myriad of ways that these concepts can be tested. I know I'm supposed to be understanding the fundamentals and I think I have it, only to be disappointed in getting the wrong answer or not knowing how to even attack the problem.

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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02 Sep 2010, 17:42

I don't have problems with other part of GMAT math, but the word problems drove me crazy like you. Espeicially those rate, distance problems. After I watched some 3-D animated problem solving videos, I realized that those problems are not hard at all. It was hard for me before because I didn't know the spacial relations well, I always get lost when going to new places. The 3-D videos show me the relations in a minutes.

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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19 Jan 2011, 06:02

First I tried to solve these using equations. It was taking too long and getting complicated. Here is how I solved some of the problems I felt tough;

2) 1. X is slower than Y in producing w widgets 2. It would have taken 4/5*2*3 =24/5 days for X and Y to build 2w widgets 3. X alone takes more than 48/5 days to produce 2w 4. Plugged in 10 first, it did not meet all constraints 5. 12 worked perfectly Answer is E.

10) 1. A is slower than B (It takes 4 more minutes to finish the same job) 2. Together they take 6 minutes to print 50 pages => It will take more than 12 minutes for A alone to print 50 pages 3. A takes more than 24 minutes to print 100 pages. 4. A might take 24 minutes to print 80 pages. 5. I plugged in 24 and it satisfied all constraints.

Re: Work Rate Questions - I collected from GMAT Club [#permalink]

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14 Sep 2011, 14:50

Machine A can fill an order of widgets in a hours. Machine B can fill the same order of widgets in b hours. Machines A and B begin to fill an order of widgets at noon, working together at their respective rates. If a and b are even integers, is Machine A's rate the same as that of Machine B? (1) Machines A and B finish the order at exactly 4:48 p.m. (2) (a + b)2 = 400

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